from The Century Dictionary and Cyclopedia

Etymologies

Examples

The conversation arrested its discursive nature, to settle upon a political chief, the highest in fame and station of that party to which Mivers professed -- not to belong, he belonged to himself alone, but to appropinquate.

Here's more: looks as though its origins are similar to that of propinquity, which comes from the Spanish propincuidad: "late 14th cent. as propinquidat; also as propincuidat (early 15th cent.), from Italian propinquità (c1200)."

So somewhere in there, the "-cuidat" appears to have become "-quidat." I'm guessing the -ate suffix on appropinquate is more modern, but the "qu" was kept.